Can pictures ever be retrieved from my dead laptop?

I have a Lenovo IdeaPad S10. It won't charge even after a new battery and power adapter so I'm assuming the charging port is busted. It's been drained of battery life for about 4 months, and I was never able to back up my very precious photos/videos. As of now I'm broke and can't bring it to a computer store. In the future, whether it be a year or 10 years, would I be able to do something, ANYTHING, to retrieve those files?

Probably the power supply is broken. You will need a new motherboard put into the laptop if you want to use it again. You could take the hard drive out of the laptop and swap it into a friend's laptop to copy your photos over to an external drive.
Also, always back up important files before its too late. I always back up important files on at least three drives. My external drive, two separate memory sticks. Also look for a free online backup website that will back your files up for you.

You can remove the hard drive and put it in an external hard drive enclosure, then plug it into a USB port on a working computer and access any files you need. External enclosures can range in price from $5 to $30, depending on how nice you want it.